We present the complete asymptotic expansion for the Kantorovich polynomials Kn as n→∞. The result is in a form convenient for applications. All coefficients of n?k (k=1,2,...) are calculated explicitly in terms of ...We present the complete asymptotic expansion for the Kantorovich polynomials Kn as n→∞. The result is in a form convenient for applications. All coefficients of n?k (k=1,2,...) are calculated explicitly in terms of Stirling numbers of the first and second kind.Moreover, we treat the simultaneous approximation with Kantorovich polynomials and determine the rate of convergence of $\tfrac{d}{{dx}}K_n (f;x) - f'(x)$ .展开更多
文摘We present the complete asymptotic expansion for the Kantorovich polynomials Kn as n→∞. The result is in a form convenient for applications. All coefficients of n?k (k=1,2,...) are calculated explicitly in terms of Stirling numbers of the first and second kind.Moreover, we treat the simultaneous approximation with Kantorovich polynomials and determine the rate of convergence of $\tfrac{d}{{dx}}K_n (f;x) - f'(x)$ .
